MIKE OSSIPOFF nkklrp-at-hotmail.com |EMlist| wrote:
Paul Kislanko kislanko-at-airmail.net |EMlist| wrote:
We're mixing terms and contexts again.
One can define majority to include all eligible voters, in which case it is
entirely possible that no alternative achieves a majority because fewer than
50 % of elegible voters participate in the election. No matter what method
is used to pick the selection of a majority of participants, it cannot be
said that the winner has been a elected by a majority.
I reply:
...What? You're not being very clear about what you mean there.
As for different kinds of majorities, I'll comment on that after I've quoted both your and Russ's objections about that.
Russ said:
My sentiments exactly.
The usage of the word "majority" by some here seems a bit inconsistent to me. In a pairwise race, the majority that seems to matter to them is *not* a majority of voters who actually *voted* on that particular pairwise race -- but rather a majority of the total number of voters who voted for other pairwise races for the same office. In other words, a majority is defined relative to the *potential* rather than the *actual* number of voters.
I reply:
For determining whether Smith pairbeats Jones, or Jones pairbeats Smith, only the ballots voting Smith over Jones or Jones over Smith are counted.
And yes, sometimes "a majority" is used as a replacement term for what we here call a pairwise defeat.
But Russ needs to undestand that that isn't the only use of "Majority". In the context of an election, the accepted meaning of "a majority" is a set of voters consisting of more than half of the voters. No, Russ, that isn't an inconsistency; it's just two different meanings.
Russ continues:
But wait just a minute.
I reply:
Ok, Russ, we're patient.
Russ continues:
If the majority that really matters is relative to the *potential* number of voters, then why isn't it defined relative to the total number of voters who voted in the entire election, including those who did not vote at all on that particular office? Or why is it not defined relative to the total number of *registered* voters? Better yet, why is it not defined relative to the total number of *eligible* voters, registered or not?
I reply:
Go for it. As you say, why not?
You'll find that, if you define a majority in one of those three other ways, Margins will still fail the four majority defensive strategy criteria, and SD, SSD, BeatpathWinner, MAM & RP will still pass all of them, and PC will still pass the ones that it passes--SFC & WDSC.
In fact, I doubt that there would be any change in which method meets the majority defensive strategy criteria.
But back to Russ's question: Why refer majority to the total number of voters in a particular race instead of the total number of voters, including the ones who didn't vote for that race, or the total number of people registered to vote, or the total number eligible to register to vote?
1. As I said, it's the accepted meaning, in the context of an election, when evaluating how many votes candidates got.
2. Of the four meanings that you could consider, including those other 3 that Russ listed, the total number of voters who voted in a particular race is the smallest number that defines a majority for which certain important strategy guarantees can be made, by some methods.
3. This is less important, but that definition of a majority simplifies examples, requiring fewer variables in examples.
A set of voters consisting of more than half of the voters in a particular race is a uniquely powerful set of voters. It's a set of voters for which certain strategy guarantees can be made.
The majority defensive strategy criteria are about such guarantees. But there are other such criteria. The familiair Majority Criterion (sometimes called Majority Winner or Majority Favorite) is another. So is the Mutual Majority Criterion.
Those guarantees are reason enough to have a name for the powerful set of voters that consists of more than half of the voters.
Russ continues:
To put it another way, when a voter intentionally abstains from voting
in a pairwise race, why is that voter still relevant in any way to the
correct interpretation of the score of that race? That's a rhetorical
question, because I'll bet that any answer will simply be a rationalization.
I reply:
Whom is that a question for? I don't have an answer to it. The methods that I propose don't give to people abstaining from a particular pairwise comparison the power to influence that pairwise comparison. Now that that issue is settled, on to another topic:
As I said above:
A set of voters consisting of more than half of the voters is a uniquely powerful set of voters--a set of voters for whom certain guarantees can be made.
That's why there are a number of criteria that refer to such a set of voters. Those include my four majority defensive strategy criteria, and other criteria too, including the Majority Favorite Criterion and the Mutual Majority Criterion.
Mike Ossipoff
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